"It it were anything other than balanced there would have to be another current induced somewhere. We just defined the situation where there was not."
No, that doesn't define coax as being a balanced feed line. It merely defines a feed line with no CMC's on it. The only similarity between coax and a balanced feed line is that it provides a path between source and load. If getting rid of those CMC's really does define a balanced feed line, you are going to have quite a few people much harder to convince of that fact than me.
- 'Doc